Adaptive Fuzzy Controller Design for Simulated Moving Bed System

1Department of Electrical Engineering, I-Shou University, No. 1, Sec. 1, Syuecheng Rd., Dashu District, Kaohsiung City 84001, Taiwan 2Electronic Information and Engineering Institute, Fujian Polytechnic Normal University, No. 1, Long Jiang Street, Fuqing City 350300, Fuzhou City, Fujian Province, China 3Department of Telecommunication Engineering, National Kaohsiung University of Science and Technology, No. 142, Haijhuan Rd., Nanzih District, Kaohsiung City 81157, Taiwan 4Department of Information Management, Cheng-Shiu University, No. 840, Chengcing Rd., Niaosong District, Kaohsiung City 83347, Taiwan


Introduction
Chromatography is a technique used for the separation of a mixture. The simulated moving bed process (SMB) has had increasing application in large-quantity supercritical fluid extraction owing to its advantages such as a low production cost, a low solvent consumption, and its ability to carry out a clean, continuous operation. (1,2) The basic principle of SMB is to use multiple columns containing the solid adsorbent and move these columns in the opposite direction to the fluid to achieve a countercurrent flow, hence the term "moving bed".
Among the chromatographic separation technologies, SMB has been recognized as a highly practical and excellent technique that requires little solvent or water while providing a high separation efficiency. (3,4) SMB is a continuous operation technique that utilizes the adsorption principle to carry out the separation. The material inlet and outlet positions of the fixed bed can be changed at a fixed switching time. Compared with other fixed adsorption systems, SMB exhibits higher production capacity and separation efficiency. An example of the separation process of SMB is shown in Fig. 1.
However, the complex and nonlinear nature of SMB still poses a challenge in precision control for researchers and developers. An adaptive nonlinear model predictive control method was proposed by Andrade Neto et al. (5) for the separation of enantiomers of praziquantel in a simulated moving bed. The primary focus of this model is to solve the problems of control speed and efficiency in the control framework.
In the classical linear model predictive controller (MPC), an improved prediction mechanism based on the strategy of switching the system was proposed by Nogueira et al. (6) The results showed that this method can control the process in both servo and regulator cases. A method of optimizing separation control to improve the product purity and economic benefit was presented in Ref. 7. Lee and Seidel-Morgenstern proposed a method based on the results of a simulation study, in which the controller can estimate the current process state and find the best operation conditions under the competitive Langmuir isotherm. (8) Yang et al. proposed an optimization strategy based on the improved moving asymptote algorithm, demonstrating that a controller based on the improved moving asymptote method can dynamically control SMB. (9) A model predictive control method applied to SMB that is based on the established state-space model was presented by Martins et al. (10)

Mathematical Model of SMB
The mathematical model of SMB can be deduced from the true moving bed (TMB) model, which is described as follows. (11,12) Table 1 gives the meanings of the SMB system's variables in the above equations. In the TMB model, the mass balance of the bulk phase is given by For SMB, the mass balance of the bulk phase is given by The model can be converted as 2 , , , From Eqs. (5) and (6), we obtain 2 , , , The adsorption equilibrium of two materials can be expressed by a linear isotherm, Effective velocity of body u s (cm min −1 ) Solid flow rate Solid phase concentration at equilibrium between solid and mobile phases Q (cm 3 Column number: 1, 2, 3, 4, 5, 6,7,8 where H i is the Henry coefficient, i = A, B, and j = 1, ..., 8. The purity formula can be calculated by   ,  , , , , , , , where C E,B represents the purity of B from the extract outlet and C R,A represents the purity of A from the raffinate outlet. The relationship between the effective velocity of the body ( j v * ) and the volume flow rate Q j is described by where d is the radius of the column and ε is the bulk void fraction.

SMB Simulation
To observe the system's behavior, a simulation of SMB is performed. The initial values of all the SMB's parameters are shown in Table 2. In this simulation, a 4-area with a 2-2-2-2 model is adopted.
Figures 2(a) and 2(b) display the variations in concentrations versus time. Figure 3 shows the concentration separation results of the two materials at the extract and raffinate outlets with different H A values.
From the results shown in Figs. 2 and 3, a high similarity can be observed between the simulation model and the real SMB system behavior. The agreement provides a promising condition for the controller we want to develop.

Adaptive Fuzzy Controller
The fuzzy theory was first proposed by Professor Lotfi Zadeh in 1965. It is a knowledgebased or rule-based system containing many fuzzy IF-THEN rules. Usually, a complete fuzzy system is mainly composed of four parts, i.e., a fuzzifier, a fuzzy rule base, a fuzzy inference engine, and a defuzzifier. (13) Fuzzy controllers have been widely employed in many linear and nonlinear control systems for their simplicity in design, especially for systems whose information is uncertain and unknown.
The control structure of the adaptive fuzzy control mechanism we developed is shown in Fig. 4. The controller is composed of two independent controllers: one is a traditional fuzzy controller and the other is a single-neuron controller. The neuron controller is used to compensate for the lack of precision control of the fuzzy controller.
In the whole SMB control process, the flow rates of Zones I (Q 1 ), II (Q 2 ), and III (Q 3 ) are controlled by three individual adaptive fuzzy controllers. The variables of purity error (e) and error change (Δe) of materials B and A used as the fuzzy inputs are defined as follows, where c E,B and c R,A are the concentrations of B and A from the extract and raffinate outlets, respectively. 1 , Three controllers can generate the increment of their own flow rate (ΔQ i , i = 1, 2, 3). Figure 5 shows the membership functions of all error terms (e i and Δe i , i = 1, 2, 3), and Fig. 6 presents the singleton membership function of the defuzzifier. Table 3 shows the fuzzy rule  table used  The second controller is the single-neuron controller, which also generates the increment of the flow rate ΔQ. As mentioned above, it is used to improve the drawback of the fuzzy controller to accomplish precision control. The model of the single-neuron controller is expressed as where y is the output of the neuron and a, b, and c are constants. Here, we set a = b = −0.1 and c = −1.

Experiments
In this study, several purity controls were implemented.

Conclusions
In this study, an adaptive fuzzy control mechanism with two independent controllers for an SMB chromatographic separation system was designed and presented. In this control mechanism, the fuzzy controller is treated as the master controller, and the neuron controller functions as a slave controller in charge of fine-tuning and improving the drawback of the fuzzy controller to implement precision control. The experimental results show that the chromatographic separation of SMB can indeed be effectively and precisely controlled by using the developed adaptive fuzzy controller. The desired purities can be obtained for the separated substances.